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20 Jul 2021, 08:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
76% (03:20) correct
24%
(03:07)
wrong
based on 413
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There are 816 students in enrolled at a certain high school. Each of these students is taking at least one of the subjects economics, geography, and biology. The sum of the number of students taking exactly one of these subjects and the number of students taking all 3 of these subjects is 5 times the number of students taking exactly 2 of these subjects. The ratio of the number of students taking only the two subjects economics and geography to the number of students taking only the two subjects economics and biology to the number of students taking only the two subjects geography and biology is 3:6:8. How many of the students enrolled at this high school are taking only the two subjects geography and biology?
(A) 35
(B) 42
(C) 64
(D) 136
(E) 240
(A) 35
(B) 42
(C) 64
(D) 136
(E) 240
20 Jul 2021, 22:36
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Exactly One+ All three=5(Exactly two).
E&G:E&B:G&B=3:6:8
Total students taking exactly two subjects=17x (x is the common ratio)
816-17x=17x*5
x=8
Students taking only geography and biology=8*x=8*8=64.
Option c.
E&G:E&B:G&B=3:6:8
Total students taking exactly two subjects=17x (x is the common ratio)
816-17x=17x*5
x=8
Students taking only geography and biology=8*x=8*8=64.
Option c.
06 Sep 2021, 05:24
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Bunuel
Solution:
Let us consider the following Venn diagram:
Attachment:
ecogeobio.png [ 11.43 KiB | Viewed 7209 times ]
Where \(a, b\) and \(c\) is the number of students taking only Economics, Geography and Biology respectively.
\(d, e\) and \(f\) is the number of students taking only Economics-Geography, Geography-Biology and Biology-Economics respectively.
And lastly, \(g\) is the number of students taking all 3 subjects.
So we are told that there are total 816 students. This means we can say \(a+b+c+d+e+f+g=816\).
We are told that sum of the number of students taking one of the subjects and the number of students taking all 3 is 5 times the students taking exactly 2 subjects. This means \(a+b+c+g=5(d+e+f)\)
Next, we are told that the ratio of the number of students taking economics and geography to the students taking economics and biology to the students taking geography and biology is \(3:6:8\). This means we can assume \(d=3x,f=6x\) and \(e=8x\).
From \(a+b+c+d+e+f+g=816\), we can write \(a+b+c+g=816-(d+e+f)=816-17x\)
We have \(a+b+c+g=5(d+e+f)\). Upon plugging the values we get:
\(⇒ 816-17x=5\times 17x\)
\(⇒ 816-17x=85x\)
\(⇒ 102x=816\)
\(⇒ x=\frac{816}{102}=8\)
Now, we are asked the number of the students taking two subjects geography and biology\(=8x=8\times 8=64\)
Hence the right answer is Option C.
